Question

I am trying a couple of tutorials from http://nehe.gamedev.net, in order to learn openGL programming, I would like to position spheres along a Bezier curve such that they appear as a string of pearls. how can I position such spheres along the curve. I am drawing the curve using de Casteljau’s algorithm and hence can get the XYZ points on the curve.

Answer 1

If your spheres are small enough relative to the overall length of the Bezier curve, you can just position your spheres at even intervals to get an appearance similar to a string of pearls. (If the spheres are relatively large then you’ll have to start worrying about sphere overlap more — not an easy problem, and probably not very instructive for learning OpenGL.)

The parameter value t of a Bezier curve varies from 0 to 1. To evaluate your Bezier curve at 10 locations (the ends and eight interior points) you can do something like this:

for( int i = 0; i <= 9; ++i )
{
    double t = i / 9.0;
    double x, y;
    EvalBezier( t, x, y );
    DrawSphere( x, y, radius );
} 

Where EvalBezier( t, x, y ) fills in (x,y) for a given t. Just pick radius to give you a pleasing result. If you want to try to pick radius automatically, just use half the minimum distance from the point i to points i-1 and i+1 as a rough estimate. If you do this, remember to handle the end points specially, using either only the next or previous points (whichever you have).